This invention relates to a method and apparatus for servomotor control, wherein the current response characteristic of a servomotor, particularly a synchronous motor, is improved.
Servomotors find wide use in a variety of fields, and in recent years A.C. servomotors have been developed. One example of an A.C motor used as a servomotor is a synchronous motor. Synchronous motors employing a permanent magnet as a rotor are coming into ever wider use since they are brushless, noiseless and simple in construction.
Synchronous motors of this type must be so controlled as to render torque constant. To this end, a technique for controlling the motor has been developed wherein a current of the same phase as the electromotive force induced by the rotor is caused to flow into the armature winding, which serves as the stator. This technique will now be described with reference to FIG. 1, which shows the construction of a synchronous motor. The magnetic flux density B at a position displaced by .theta. degrees from the q axis of the magnetic field generated by a rotor 1, namely a permanent magnet, is given by the following: EQU B=B.sub.m sin.theta. (1)
The magnetic flux .phi. interlinked with the a winding of a stator 2 shown in FIG. 1 is expressed as follows: EQU .phi.=-.phi..sub.m cos.theta..sub.c ( 2)
where .phi..sub.m represents the magnetic flux on the q axis of the rotor 1. Accordingly, the electromotive force e.sub.1 induced in the a winding is expressed as follows: ##EQU1## where .theta.=P.theta.m=P.multidot..omega..sub.m .multidot.t.
Likewise, the electromotive forces e.sub.2, e.sub.3 induced in the b and c windings of the stator 2, which are disposed at angles of 1/3.pi. and 2/3.pi. relative to the a winding, respectively, are expressed by the following: EQU e.sub.2 =-.phi..sub.m .multidot.P.multidot..omega..sub.m .multidot.sin(.theta.-2/3.pi.) (4) EQU e.sub.3 =-.phi..sub.m .multidot.P.multidot..omega..sub.m sin(.theta.-4/3.pi.) (5)
If we let the currents flowing in the armature windings a, b, c be represented by i.sub.1, i.sub.2, i.sub.3, respectively, then the output torque T of such a three-phase synchronous motor will be expressed by the following: EQU T=1/2(e.sub.1 .multidot.i.sub.1 +e.sub.2 .multidot.i.sub.2 +e.sub.3 .multidot.i.sub.3) (6)
Therefore, substituting Eqs. (3), (4) and (5) into Eq. (6), we have: ##EQU2## To render the torque T constant, T should be independent of the angle Q. Therefore, if the following relations hold, namely: ##EQU3## where I is the current amplitude, then T may be written as follows, from Eq. (7): ##EQU4## Thus, the torque T is constant, being independent of the rotational orientation of the rotor 1.
To carry out such control, it is necessary to detect the rotor angle of the synchronous motor and regulate each of the armature current values in accordance therewith.
However, if the current flowing through each armature winding happens to be delayed by .phi..sub.o from the ideal value, then the currents i.sub.1, i.sub.2, i.sub.3 of the respective armature windings will take on the form: EQU i.sub.1 =Isin(.theta.-.phi..sub.o) EQU i.sub.2 =Isin(.theta.-2/3.pi.-.phi..sub.o) ##EQU5## In consequence, the output torque T will take on the form: ##EQU6## from which it will be understood that the torque decreases in value.
Thus, in order to render the torque of a synchronous motor constant, it is necessary to improve the actual current response for each current command. Specifically, as shown in the block diagram of FIG. 2 illustrating a synchronous motor control circuit according to the prior art, the actual rotational velocity v of a synchronous motor 101 is detected, the difference between v and a commanded velocity VCMD is found by an arithmetic unit 105, the velocity difference obtained is converted into a current command I by a velocity loop operational circuit 106, thereafter the difference between the current command I and the actual current i flowing into the synchronous motor 101 is computed by an arithmetic unit 110, the current difference is operated upon by a current loop operational circuit 113, and the output of the operational circuit 113 is power amplified by a pulse width modulator/inverter circuit 115, with the output of the circuit 115 being applied to the synchronous motor 101. The effect of this arrangement is to improve the frequency characteristic of the current loop and provide a more satisfactory actual current response with respect to the current command. If the synchronous motor 101 is expressed in terms of a transfer function, as shown in FIG. 2, the current loop includes feedback from the velocity v, which is attributed to the back electromotive force constant Ke of the motor. In FIG. 2, TR represents load torque, and La, Ra, Kt, J denote transfer constants. This velocity feedback has an effect upon the actual current. At high velocity, the current loop is influenced by the velocity v, resulting in a less than satisfactory actual current response.
More specifically, let us consider motor acceleration, with reference being had to FIG. 3. In a situation where the velocity feedback is negligible, velocity v and actual current i make ideal transitions at each point in time t, as indicated by the dashed lines. Owing to velocity feedback, however, the actual current i is influenced by the velocity v, as shown by the solid line in FIG. 3(b). The disadvantageous results are an enlarged current magnitude and prolonged acceleration time.